M. Pino

activity

20062025

most citedEntire Solutions of the Allen-Cahn equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in

R^{3}

14 citations · 89 across the 19 of their papers we have counts for

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Showing 2017 · math.APShow all

2 papers · 2 filters

math.AP2017

Ancient shrinking spherical interfaces in the Allen-Cahn flow

Manuel del Pino, Konstantinos T. Gkikas

We consider the parabolic Allen-Cahn equation in $R^{n}$ , $n \geq 2$ , $u_{t} = Δ u + (1 - u^{2}) u in R^{n} \times (- \infty, 0] .$ We construct an ancient radial…

math.AP2017★ 2 cited

Ancient multiple-layer solutions to the Allen-Cahn equation

Manuel del Pino, Konstantinos T. Gkikas

We consider the parabolic one-dimensional Allen-Cahn equation $u_{t} = u_{xx} + u (1 - u^{2}) (x, t) \in R \times (- \infty, 0] .$ The steady state $w (x) = tanh (x / 2)$ , co…